Arun
Last Activity: 6 Years ago
Escape velocity of a projectile from the Earth, vesc = 11.2 km/s
Projection velocity of the projectile, vp = 3vesc
Mass of the projectile = m
Velocity of the projectile far away from the Earth = vf
Total energy of the projectile on the Earth = (1/2)mvp2 – (1/2)mvesc2
Gravitational potential energy of the projectile far away from the Earth is zero.
Total energy of the projectile far away from the Earth = (1/2)mvf2
From the law of conservation of energy, we have
(1/2)mvp2 – (1/2)mvesc2 = (1/2)mvf2
vf = ( vp2 – vesc2 )1/2
= [ (3vesc)2 – vesc2 ]1/2
= √8 vesc
= √8 × 11.2 = 31.68 km/s.
